Problem 90 - Elementary and Intermediate Algebra

Question

Use a calculator to find each value. Give answers to four decimal places. See Using Your Calculator: Evaluating Logarithms. $$ \log 375.876 $$

Step-by-Step Solution

Answer

The value of \( \log 375.876 \) is approximately 2.5744.

Step 1: Understand the Problem

We need to calculate the common logarithm of the number 375.876 using a calculator. The common logarithm is the logarithm to the base 10, denoted as \( \log \).

Step 2: Use the Calculator for Calculation

Enter the number 375.876 into the calculator and use the logarithm function, often labeled as 'log' or 'log10', to compute its logarithm.

Step 3: Record the Answer

Write down the result displayed by the calculator, ensuring it is correct to four decimal places.

Key Concepts

Calculator Use

Using a calculator to find logarithms is straightforward once you understand the basic functions of your device. Calculators usually have a key labeled 'log' or 'log10,' which is specifically for common logarithms, or log base 10.

• First, turn on the calculator and ensure it's in the standard mode for numerical calculations.
• Next, enter the number you wish to find the logarithm of—in this case, 375.876.
• Press the 'log' or 'log10' button, and the calculator will instantly compute the logarithm for you.
• The displayed result is typically formatted to a few decimal places.

This functional approach allows you to quickly and accurately calculate logarithms without needing a deep understanding of the logarithmic concept itself.

Common Logarithm

A common logarithm is a logarithm with base 10. It is commonly used in scientific calculations and is simply denoted as \( \log x \). The beauty of common logarithms is in their wide application and ease of use with calculators, as most scientific calculators are equipped to handle them. In the expression \( \log 375.876 \), you are essentially asking the question: "10 raised to what power equals 375.876?"Key Points:

• Common log is logarithm base 10.
• Often used for simplifying calculations, especially in pH in chemistry or decibels in acoustics.

Understanding how logarithms help us convert multiplicative relationships into additive ones can simplify solving equations and even help to work with extremely large or small numbers efficiently.

Decimal Places

When the exercise requires an answer to be given to four decimal places, accuracy and precision are crucial. Decimal places are the digits that appear after the decimal point in a number. For this exercise:

• After using the calculator, you'll receive a number.
• Make sure to check the number of decimal places and adjust if necessary.
• For example, if the computed value of \( \log 375.876 \) is 2.574966, you would round and write it as 2.5750. Rounding is required to ensure the answer is formatted to the specified count of decimal places.

Maintaining the precision of four decimal places is important in academic contexts, particularly in fields like statistics and engineering, where the smallest differences can significantly impact results.